Mathematics Reasoning Long Questions (Question 1 - 3)


Question 1:
(a) State if each of the following statements is true or false.
     (i) 2 4 =16  and  12÷ 27 3 =3.
     (ii) 17 is a prime number or an even number.

(b) Complete the statement, in the answer space, to form a true statement by
      using the quantifier ‘all’ or ‘some’.

(c) Write down two implications based on the following statement:

A number is a prime number if and only if it is only divisible by 1 and itself.

Solution:
(a)(i) False
(a)(ii) True

(b)   Some      multiples of 3 are multiples of 6.

(c) Implication 1: If a number is a prime number, then it is only divisible by 1
                             and itself.
     Implication 2: If a number is only divisible by 1 and itself, then it is a prime
                             number.



Question 2:
(a) State if each of the following statements is true or false.
      (i)  2 × 3 = 6 or 2 + 3 = 6
      (ii) 2 is a prime number and 5 is an even number.

(b) Write down the converse of the following implication.
      Hence, state whether the converse is true or false.

If x is a multiple of 12,
then x is a multiple of 3.

(c) Complete the premise in the following argument:

Premise 1: All hexagons have six sides
Premise 2: _____________________
Conclusion: ABCDEF has six sides.

Solution:
(a)(i) True
(a)(ii) False

(b) Converse: If x is a multiple of 3, then x is a multiple of 12.
      The converse is false.

(c) Premise 2: ABCDEF is a hexagon.




Question 3:
(a) Complete each of the following statements with the quantifier ‘all’ or ‘some’
      so that it will become a true statement.
      (i) ___________ of the prime numbers are odd numbers.
     (ii) ___________ pentagons have five sides.

(b) Write down two implications based on the following statement:

AB = B if and only if A υ B = A.

(c) Complete the premise in the following argument:

Premise 1: If a number is a factor of 24, then it is a factor of 48.
Premise 2: 12 is a factor of 24.
Conclusion: _____________________


Solution:
 (a)(i)       Some      of the prime numbers are odd numbers.
 (a)(ii)        All         pentagons have five sides.

(b) Implication 1: If AB = B, then A υ B = A.
      Implication 2: If A υ B = A, then AB = B.

(c) Conclusion: 12 is a factor of 48.